Numerical study of localized impurity in a Bose-Einstein condensate

Abstract

Motivated by recent experiments, we investigate a single ${}^{133}\text{Cs}$ impurity in the center of a trapped ${}^{87}\text{Rb}$ Bose-Einstein condensate. Within a zero-temperature mean-field description we provide a one-dimensional physical intuitive model which involves two coupled differential equations for the condensate and the impurity wave function, which we solve numerically. With this we determine within the equilibrium phase diagram spanned by the intra- and inter-species coupling strength, whether the impurity is localized at the trap center or expelled to the condensate border. In the former case we find that the impurity induces a bump or dip on the condensate for an attractive or a repulsive Rb-Cs interaction strength, respectively. Conversely, the condensate environment leads to an effective mass of the impurity which increases quadratically for small interspecies interaction strength. Afterwards, we investigate how the impurity imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the impurity-induced bump in the condensate wave function starts decaying marginally, whereas the dip decays with a characteristic time scale which decreases with increasing repulsive impurity-BEC interaction strength. Secondly, once the attractive or repulsive interspecies coupling constant is switched off, we find that white-shock waves or bi-solitons emerge which both oscillate within the harmonic confinement with a characteristic frequency.

arXiv admin note: text overlap with arXiv:1508.05482

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• OpenMP Fortran and C programs for solving the time-dependent Gross-Pitaevskii equation in an anisotropic trap
• OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross-Pitaevskii equation
• Induced correlations between impurities in a one-dimensional quenched Bose gas
• Multispecies time-dependent restricted-active-space self-consistent-field theory for ultracold atomic and molecular gases
• Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons
• Collision of impurities with Bose-Einstein condensates
• Gray/dark soliton behavior and population under a symmetric and asymmetric potential trap
• Slow sound in matter-wave dark soliton gases
• PT-Symmetric potential impact on the scattering of a Bose-Einstein condensate from a Gaussian Obstacle
• A distinguishable single excited-impurity in a Bose-Einstein condensate
• Shape of a sound wave in a weakly-perturbed Bose gas
• Impurity induced Modulational instability in Bose-Einstein condensates
• Thermalization of isolated Bose-Einstein condensate under a PT-symmetric environment
• Quantum dynamics of impurities in a Bose-Einstein condensate
• Anisotropic potential immersed in a dipolar Bose-Einstein condensate
• Retroreflection and diffraction of a Bose-Einstein condensate by evanescent standing wave potential